Kohli's Reversion to his Old Mistakes
Kohli's lack of form is because of a recurrence in a problem he used to face with his head falling over. His stance is slowly reverting back to that which brought him a lot of failures on the 2014 tour to England, where he was eaten alive by Anderson.
This is on Day 4 of the 3rd test, the delivery he almost got out to bowled by Anderson. Look at where the foot is placed. Due to that exaggerated movement of the foot, his instincts are telling him that the stumps are further out than they should be, prompting him to try and defend the ball which is in fact nowhere near the stumps. That shuffle across only works on a pitch that isn't really swinging, it's asking for trouble in English conditions. You can also see to what extent his head is falling over, dragging him towards deliveries that shouldn't be played on the front foot.
This is the delivery on the same day of the test match that he got out to. Once again, just look where the bat is and where the body is. On this occasion, he didn't move his feet and genuinely had a lapse in concentration to flirt with a delivery that he had no business playing. However, the technical fault I mentioned comes into play, since this delivery is at the same height for a cut shot, a safer option in these conditions where the bounce was relatively constant. Kohli's limited range of strokes on the off-side, especially regarding the back-foot range of strokes, is preventing him from scoring runs against an English lineup he should be dominating. Again, though it is less prominent, we can see his head falling over.
This is on Day 1 of the 3rd Test Match where we can again see how far across his head is compared with the rest of his body. His foot movement this time was not to the line of the ball, forcing him to overcompensate and try and drive it when it shouldn't have been considered in the first place. If you look at where he's playing that drive, it's too straight and it doesn't create a chance for the batter to at least salvage some runs from a risky stroke.
This is from Day 1 of the 1st test match, where we can yet again see that his foot movement places him in a situation of uncertainty where he does not recognize how far across from his stumps he is actually playing.
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To conclude, Kohli's lack of runs in test cricket, especially this series, is due to his awkward foot movement and wayward head position. He is a beast of an athlete and has a very strong mentality with aggression, but his coaches and analysts need to do a better job and show him where he is struggling. He had similar issues in 2014 against England, and he overcame those issues. He has the attitude and determination to do so again, but he needs better coaches around him to prevent this from recurring and to fix the problem before it becomes a habit.
If I had the connections I'd tell him this, especially since the dismissal pattern can be rectified with a few minor adjustments. However, one thing to note is that by covering up a flaw in your technique, you will expose something else which must be worked on. There is no perfect technique in test cricket, but for Kohli, he has the mental strength to outlast a poor patch of form. A few improvements in his technique should bring him back to his best.
I would suggest that he lets the bowler see his off-stump instead of shuffling across to cover that type of dismissal. It will allow him to make a better judgement of which deliveries to play, and how to do so. Fixing his back-foot game on the off-side will require a lot more work, but minor adjustments to the technique and stance will surely get him the runs he so desperately needs.
Note that all the images are from the England and Wales Cricket Board Youtube Channel. I do not own any of the images.